Cluster Synchronization of Boolean Control Networks With Reinforcement Learning

State-flipped control for cluster synchronization of Boolean control networks (BCNs) is considered in this brief. When the reachable set of the target set is empty or the reachable set does not cover all states of the network, state-flipped control is used to achieve cluster synchronization and a corresponding theorem is given. When dealing with large-scale networks, Q-learning
$(QL)$
is a model-free reinforcement learning method that can be used to find optimal control sequences. It can stabilize the network to a target set with minimum cost for cluster synchronization. The theoretical results are verified by a numerical example in the end.